
where, for \(n=0\) , we interpret \(\delta _{x_1}+\cdots +\delta _{x_n}\)  as the zero measure.
By the multivariate Mecke equation ([1]}), this equals
\(\sum ^\infty _{n=0}&\int f(\delta _{x_1}+\cdots +\delta _{x_n})\prod ^n_{i=1}p(x_i,\delta _{x_1}+\cdots +\delta _{x_n})P(x_1,\ldots ,x_n)\,\lambda _n(\mathrm {d}(x_1,\ldots ,x_n)),\) 
